Difficulty: Easy
Correct Answer: 308
Explanation:
Introduction / Context:
This question uses the fundamental relationship between the product of two numbers, their highest common factor (H.C.F.), and their least common multiple (L.C.M.) to find an unknown number. It is a very standard pattern in aptitude exams and can be solved quickly if you remember the key identity.
Given Data / Assumptions:
Concept / Approach:
For any two positive integers a and b, their product satisfies the identity a * b = H.C.F. * L.C.M. When we know one of the numbers and both the H.C.F. and L.C.M., we can find the other number by rearranging this identity. This avoids the need for any complicated factorization.
Step-by-Step Solution:
Step 1: Let the unknown number be x and the known number be 275.Step 2: Given H.C.F. = 11 and L.C.M. = 7700.Step 3: Use the relation 275 * x = H.C.F. * L.C.M. = 11 * 7700.Step 4: Compute the right side: 11 * 7700 = 84700.Step 5: So 275 * x = 84700.Step 6: Solve for x: x = 84700 / 275.Step 7: Perform the division: 84700 ÷ 275 = 308.Step 8: Therefore, the other number is 308.
Verification / Alternative check:
Check product: 275 * 308 = 84700.Check H.C.F. of 275 and 308: gcd(275, 308) = 11.Check L.C.M.: (product) / H.C.F. = 84700 / 11 = 7700. All conditions are met, so 308 is consistent with the given H.C.F. and L.C.M.
Why Other Options Are Wrong:
Options a (279), b (283), and d (318) do not satisfy the identity a * b = 11 * 7700 when paired with 275. Either their product with 275 is not 84700, or their greatest common divisor with 275 is not 11, so they cannot be correct answers.
Common Pitfalls:
Some students misremember the formula and incorrectly use H.C.F. + L.C.M. or some other operation instead of the product. Others make arithmetic mistakes while multiplying 11 by 7700 or when dividing by 275. Carefully applying the correct identity and doing the arithmetic step by step ensures an accurate result.
Final Answer:
The other number is 308.
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